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This article addresses a problem of micromagnetics: the reversal of magnetic moments in layered spring magnets. A one-dimensional model is used of a film consisting of several atomic layers of a soft material on top of several atomic layers of a hard material. Each atomic layer is taken to be uniformly magnetized, and spatial inhomogeneities within an atomic layer are neglected. The state of such a system is described by a chain of magnetic spin vectors. Each spin vector behaves like a spinning top driven locally by the effective magnetic field and subject to damping (Landau-Lifshitz-Gilbert equation). A numerical integration scheme for the LLG equation is presented that is unconditionally stable and preserves the magnitude of the magnetization vector at all times. The results of numerical investigations for a bilayer in a rotating in-plane magnetic field show hysteresis with a basic period of $2pi$ at moderate fields and hysteresis with a basic period of $pi$ at strong fields.
We present a novel mathematical approach to model noise in dynamical systems. We do so by considering dynamics of a chain of diffusively coupled Nagumo cells affected by noise. We show that the noise in transmembrane current can be effectively modell
We present a convergence proof of the projective integration method for a class of deterministic multi-dimensional multi-scale systems which are amenable to centre manifold theory. The error is shown to contain contributions associated with the numer
Extended dynamic mode decomposition (EDMD) provides a class of algorithms to identify patterns and effective degrees of freedom in complex dynamical systems. We show that the modes identified by EDMD correspond to those of compact Perron-Frobenius an
Massive parallelisation has lead to a dramatic increase in available computational power. However, data transfer speeds have failed to keep pace and are the major limiting factor in the development of exascale computing. New algorithms must be develo
In order to analyze structure of tangent spaces of a transient orbit, we propose a new algorithm which pulls back vectors in tangent spaces along the orbit by using a calculation method of covariant Lyapunov vectors. As an example, the calculation al